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Theorem bnj1071 31591
Description: Technical lemma for bnj69 31624. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1071.7 𝐷 = (ω ∖ {∅})
Assertion
Ref Expression
bnj1071 (𝑛𝐷 → E Fr 𝑛)

Proof of Theorem bnj1071
StepHypRef Expression
1 bnj1071.7 . . 3 𝐷 = (ω ∖ {∅})
21bnj923 31384 . 2 (𝑛𝐷𝑛 ∈ ω)
3 nnord 7334 . 2 (𝑛 ∈ ω → Ord 𝑛)
4 ordfr 5978 . 2 (Ord 𝑛 → E Fr 𝑛)
52, 3, 43syl 18 1 (𝑛𝐷 → E Fr 𝑛)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1658  wcel 2166  cdif 3795  c0 4144  {csn 4397   E cep 5254   Fr wfr 5298  Ord word 5962  ωcom 7326
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-8 2168  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2803  ax-sep 5005  ax-nul 5013  ax-pr 5127  ax-un 7209
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3or 1114  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ne 3000  df-ral 3122  df-rex 3123  df-rab 3126  df-v 3416  df-sbc 3663  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-pss 3814  df-nul 4145  df-if 4307  df-sn 4398  df-pr 4400  df-tp 4402  df-op 4404  df-uni 4659  df-br 4874  df-opab 4936  df-tr 4976  df-eprel 5255  df-po 5263  df-so 5264  df-fr 5301  df-we 5303  df-ord 5966  df-on 5967  df-lim 5968  df-suc 5969  df-om 7327
This theorem is referenced by:  bnj1030  31601  bnj1133  31603
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